Thursday, March 30, 2006

Modal Plenitude and Rationalism

Intuitively, there are a vast number of possibilities, or 'ways a world could be'. The principle of plenitude says that there are enough possible worlds to cover all these vastly many possibilities, so that we aren't left with any "gaps" in modal space. But reductionists have trouble retaining this as a substantive principle. David Lewis claims that a possibility just is a world, and takes the latter as basic. So the simple statement of plenitude becomes equivalent to the trivial claim that there are as many worlds as there are, um, worlds. As Lewis admits: "That would be true even if there were only seventeen worlds, or one, or none. It says nothing at all about abundance or completeness." (On the Plurality of Worlds, p.86.)

But then, it seems, the reductionist can't really take their possible worlds as basic -- at least, not conceptually. They must define the breadth of their content against some other (rationally accessible) standard. Lewis himself opts for a "principle of recombination according to which patching together parts of different possible worlds yields another possible world." (p.87) We have horses, and horns, so we can stick them together to establish the possibility of unicorns.

(Lewis also wants to allow for the possibility of "alien" properties or individuals, that cannot be constructed out of actual world parts, but he doesn't have any way to specify or generate them. At best, he can apply the recombination rule to any given alien world, so that "[i]f there are some, there are many more." (p.92) But for all he says, there could be gaps in his modal space where possible alien worlds should be, but simply happen not to be in fact. He is thus unable to state - and meet - a fully adequate principle of plenitude.)

Let's be generous and grant that the reductionist can come up with an adequate principle of plenitude, which spells out - in nonmodal terms - how to generate the entire breadth of possibilities. It then seems that it is this specification, rather than the space of "possible worlds", which grounds his theory of modality. But note that the adequacy of any such specification depends upon its ability to accommodate our modal intuitions (about the full breadth of possibility) that hold upon rational reflection. As such, we seem left with the result that it is really this rational standard that grounds the breadth of possibility. That is, we are led away from worlds-based reductionism, and towards a form of modal rationalism.



  1. On second thought: lacking the appropriate concepts, we presumably also lack rational access to various "alien" possibilities. But we can overcome this flaw by appeal to primitive modality. (The idealized rational agent would then grasp all possible concepts, etc.) Though, having made this move, it seems to be the primitivism, and not the rationalism, that's doing the real work here.

  2. Lewis of course wants to avoid primitive modality. But he also wants to endorse alien possibilities. As you notice, this leads to a tension in his position. This tension is distinct from the tension between appealing to intuition to justify plenitude, and the modal realist's attitude to worlds as ontologically primary and existing independently of us.

    For the former tension, see 'The analytic limit of genuine modal realism' by Divers and Melia. The latter tension has been noticed by several people, including Chihara in his book.

    If we want to retain modal realism we need an independent restriction on the number of worlds. I tend towards the idea that the laws of physics should do the job. Of course this requires necessetarianism about laws...


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